Lecture03_winter09

# Lecture03_winter09 - TIME VALUE OF MONEY APPLICATION PV is...

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TIME VALUE OF MONEY

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APPLICATION PV is used to trade different schedules of cash flows. You were willing to trade \$542,049 today for 20 annual payments of \$63,663 because they have the same Present Value . Principle being applied:”Assets of equal value trade”.
APPLICATION 2 Present Value can also be used to choose between two different schedules of payments. Principle in use:” You prefer to hold an asset with a higher Present Value of Cash Flows”

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APPLICATION 2 CHAPTER 4, PROBLEM 54 You have recently won the super jackpot in the Washington State Lottery. On reading the fine print, you discover that you have two options: You can receive 31 annual payments of \$160,000, with the first payment being received today. The income will be taxed at 28% You will receive \$446,000 now and starting next year, receive \$101,055 for 30 years. The income is taxed at 28% too. The discount rate is 10%
APPLICATION 2 ) 28 . 0 1 ( * * 000 , 160 \$ 000 , 160 \$ ) 1 ( 30 % 10 A Option PV ) 28 . 0 1 ( * * 055 , 101 \$ 000 , 446 \$ ) 2 ( 30 % 10 A Option PV

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APPLICATION 2 PV(Option 1)=\$1,201,180.55 PV(Option 2)=\$1,131,898.53 You should choose Option 1, because it has the Highest Present Value.
Growing Perpetuity Is a perpetual stream of Cash Flows. The first Cash Flow will start one period from now and will occur with the same periodicity. The Cash Flows will grow at a constant rate of g% What is the Present Value of this stream of Cash Flows if the interest rate is r%? Year 0 1 2 3 T T+1 Cash C C(1+g) 1 C(1+g) 2 C(1+g) T-1 C(1+g) T

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The Sum of the Present Value of the Cash Flows in this Growing Perpetuity is just the Sum of a Geometric Series of rate (1+g)/(1+r). The Sum of such series is C/(r-g) For this Sum to work you need r>g. Why?
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## This note was uploaded on 01/28/2012 for the course ECON 134a taught by Professor Lim during the Winter '08 term at UCSB.

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Lecture03_winter09 - TIME VALUE OF MONEY APPLICATION PV is...

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